Talk:Conic optimization

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I am not sure what is the standard nomenclature in the literature, or even whether there is a standard, but all the instances of conic optimization I stumbled upon had a linear objective function and they were called Linear Conic Optimization problem. It seems to me that, if the objective function is convex and non-linear, its nonlinearity can be "hidden" inside the convex cone and so we may replace the convex objective function by a linear one.

I have also come across something called a Nonlinear Conic Optimization problem, but that was much more involved and its definition mentioned a C-convex function, where C is an arbitrary convex set (convex functions are ${\displaystyle \mathbb {R} _{+}}$-convex functions, where ${\displaystyle \mathbb {R} _{+}}$ are the nonnegative reals).

I wonder if it is a good idea to restrict the definition of conic optimization problems to have linear objective functions, or maybe split this page to mention both the linear and nonlinear forms.

--Marcelkcs (talk) 16:16, 4 June 2011 (UTC)Reply